Math Word Problems:

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Math Playground!

Overview/Characteristics:

· Combination of words and math symbols used together to create a problem or situation where solutions must be found
· Referred to as story problems due to the fact that they created real-life scenarios
· Requires computational knowledge and literacy skills to be solved with a given problem
· Students are expect4ed to read and understand the language of the problem
· Students must identify the question in word problems
· Students must pull out essential numerical information and ignore extra information
· Students must choose a method to solve the math problem, find a solution, and check to see whether the answer makes sense
· Combines mathematical and reading skills in which information requires close examination and attention to detail



Teaching Tips:
· In younger grades, create problems that are based on children’s own experiences. Teachers should base word problems on their everyday experiences that are relatively easy to solve.
· In middle to higher grades, create problems that are more nonroutine. Nonroutine problems include multiple steps, extra information, lack of essential information, or have more than one correct answer. These problems provide students the chance to exercise their ability to think critically about the problem as they practice their math skills and prepare themselves for real-life situations.
· Similar to how we use scaffolding and thinking aloud during comprehension reading strategies, thinking aloud to solve math word problems will help students become skilled problem solvers. In addition, questioning techniques such as, “What is the problem asking?” or “What is the next step we should take?” helps students learn how to question the problem on their own. Combining these two techniques leads to full comprehension for students.
· Most textbooks recommend some variation of “read, plan, solve, and look back.” Often times, this process is not helpful enough to students, so it is beneficial if the teacher incorporates choral reading, think alouds, and line by line reading.


Activity/Word Problem Example:
Teachers can use read alouds and generate word problems used from the text descriptions.

For example:
A third grade teacher selected the book Tiger Math: Learning to Graph from a Baby Tiger to read aloud. The book tells the real life story of T.J., a Siberian tiger born at a zoo. The right side pages of the book provide the actual “story” while the left side pages illustrate a variety of picture, bar, and circle graphs that complement the text. The teacher read the story to the class in order to engage the learners with the content. She stopped periodically throughout the text to ask questions in the form of word problems such as the following:
The book tells us that T.J. weighed only 3 pounds at birth. He was very tiny in comparison to his mother, Buhkra, who weighed 250 pounds, and his father, Matthew, who weighed 350 pounds. How much more did T.J.’s father weigh than his mother?

Steps to help students solve math word problems generated from text:
· Model thinking
· Highlighting questions with color coding
· Rewriting the equation
· Checking back to see if the answer makes sense



Graphic Organizers:
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Math Picture Books:
Overview:
Math picture books are great to use in math education because they often verbalize the concepts that students have difficulty understand­ing and show these concepts visu­ally. Picture books about math also display practical uses for math skills in daily life. Educators are often looking for ways to integrate math into their literature-based lessons, and picture books with math concepts offer an excellent way to include math in other curriculum areas.


Characteristics:
- Math concepts hidden within the story (The Doorbell Rang)
- Develop ideas behind real-life math (One Grain of Rice)
- Focuses on one math concept (Subtraction Action)
- Vibrant , bold, illustrations (Each Orange Had Eight Slices)
-Simple sentences (12 Ways to Get to 11)
-Offers tips and hints
-Suggestions and extensions at end (Amanda Bean’s Amazing Dream: A Mathematical Story)
-Provides possibilities for hands on activities (Fraction Fun)


Examples of Math Picture Books:
Number Sense: How Much is a Million by David M. Schwartz
Counting: 12 Ways to Get to 11 by Eve Merriam
Measurement: Jim and the Beanstalk by Raymond Briggs
Patterns: The Keeping Quilt by Patricia Polacco
Geometry: Circus Shapes by Stuart J. Murphy
Money: The Coin Counting Book by Rozanne Williams
Place Value: Sir Cumference and all the King’s Tens by Cindy Neuschwander
Addition: Animals on Board by Stuart J. Murphy
Subtraction: Candy Counting by Lisa McCourt
Multiplication: Amanda Bean’s Amazing Dream: A Mathematical Story by Cindy Neuschwander
Division: The Doorbell Rang by Pat Hutchinson Estimating: Betcha! Estimating by Stuart J. Murphy

Feel Free To Use These Books For Your Research!
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Works Cited:

McMcDonald, Sheri . "Picture Books + Math = Fun." American Library Association. Nov. 2004. 4 Mar. 2010. <http://www.ala.org/ala/aboutala/offices/publishing/booklinks/resources/PictureBooksPlusMath.pdf>.

Moss, Barbara, and Diane Lapp. Teaching New Literacies in Grades K-3
. New York: The Guilford Press, 2010.

Moss, Barbara, and Diane Lapp. Teaching New Literacies in Grades 4-6. New York: The Guilford Press, 2010.


"Picture Books For Math." Childrens Picture Books. 2007. 3 Mar. 2010. <http://childrenspicturebooks.info/articles/picture_books_for_math.htm>.


Students' Responses:
Megan Garlette Title: Subtraction Action by Loreen Leedy
Citation: Leedy, L. (2000). Subtraction Action. New York: Holiday House.
Reading Level: DRA: 24 Guided Reading: K Grade: 2
Suggested Literacy Strategy: Students could use the summarizing strategy after reading this story. There is a lot of information covered and a lot of examples are given. Students could be asked to describe two important situations in which subtraction is used.
Description: This book details a number of topics that may confuse children about subtraction and includes a comic like set up to teach children basic components important to successful subtraction. The book is humorous and the comic set up may engage learners and show them how subtraction can be used in their everyday lives.

Kaitlin Farrell
Citation
: Pluckrose, H. (1994). Math Counts: Length. Chicago, IL: Children’s Press.
Reading Level: K-3
Suggested Literacy Strategy: Main Idea; Because the book contains many different smaller ideas that relate to measurement, it would be good for students to try to figure out the main idea.
Description: This book is for young children who are just beginning to learn about basic mathematical concepts such as measurement. Although the title suggests otherwise, this book focuses on two specific types of measurement- length and height. The text discusses why people measure things, what length/height are used to measure, and how people measure length/height. These concepts are enforced by large pictures. It includes many measurement units such as inches and centimeters to miles an kilometers. However, the main differences between length and height are not touched upon explicity. In addition, the book does not explain that there are two ways to measure objects in the United States: either by using the metric system or the standard system. Rather, the units are explained together. This book serves mainly revolves around the idea that in our society, people “need to measure things to find out exactly how long they are.”

Jeanna Calia
Book: Anno’s Mysterious Multiplying Jar by Masaichiro and Mitsumasa Anno
Citation: Anno, M., & Anno, M. (1983). Anno's Mysterious Multiplying Jar. New York: Philomel Books.

Description:
This math picture book is the best way to explain factorials to children. The book illustrates how many jars there are in the boxes on an island. It goes through all of the steps very simply and makes everything clear. It’s a great way of illustrating to readers the explanation of the concept of multiplying visually, especially for visual learners. At the end of the book, the author goes into great detail of how to solve 10 factorial using a specified system and helpful diagram.
Reading Level: DRA: 38 Guided Reading: P Grade Level Equivalent: 3.1
Suggested Literacy Strategy: Students can use the look back and fix it technique in which they can go back into the text and try and figure out how to use their multiplying skills from the beginning of the story. This book requires a lot of time and focus in order to fully understand the math concept being introduced.



Jen Levine
Book: The Doorbell Rang by Pat Hutchins
Citation: Hutchins, Pat. (1986). The Doorbell Rang. New York, NY: Mulberry Books.
Description: The Doorbell Rang is about a mother who makes a batch of twelve cookies for her two children. Their mother tells them to share so they calculate that they each get six cookies. However, every time the doorbell rings, more people come and they have to keep equally sharing the twelve cookies. Eventually, each person only gets one cookie, that is, until their grandma comes with more cookies to share.
Reading Level: Guided Reading Level: J; DRA Level: 18-20; Ages 4-8
Suggested Literacy Strategy: Students can use the predicting comprehension strategy for this book. The students can predict what they think will happen each time the doorbell rings and use math skills to predict how many cookies each child will get.


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Debra Szubrowski
Book: Millions to Measure
Citation: Schwartz, David M. (2003). Millions to Measure. New York, NY: Harper Collins
Reading Level: Grades 3-5
Description: This book is about measurement and its history. Children travel back in time with a magician in a hot balloon. They travel to prehistoric times where people used stones and their feet to measure, then to medieval times where the kings created standards for measurement and rulers, then to the 1700s when the metric system was invented and then to the present. Besides talking about the history, the book uses text and illustrations to help children understand the units of measurement such as feet, yards, pounds, cups, pints, etc. and when to use them. It also talks about the metric system.
Suggested Literacy Strategy: Readers can use the summarizing strategy because the book contains many details and different ideas about measurement. By summarizing, they could find the most important information in the book.

Randee Myers
Book: Benny’s Pennies by Pat Brisson
Citation: Brisson, P. (1995). Benny’s Pennies. New York, NY: Bantam Doubleday Dell Books for Young Readers.
Reading Level: DRA: 13-14; Guided Reading: H
Description: Benny McBride had five shiny new pennies and did not know what to buy with them. He asked his mother, his brother, his sister, his dog and his cat for advice. With their suggestions in mind, Benny strolled around town and bought five new items with each of his five pennies to surprise his family members.
Suggested Literacy Strategy: In this math picture book, the simple concept of subtraction is addressed in the story. Benny started with a total of five pennies and as he bought each item, his collection of pennies decreased by one. The strategy of predicting could be utilized to help students better understand the concept. As students read the book, they can predict what will happen to Benny’s pennies each time he buys an item. This will help them to visualize the pattern of subtracting one each time.


Tom Medvecky
Book: Math Curse
Citation: Scieszka, J and Smith, L. (1995). Math Curse. New York, NY. Pengin Books.
Reading Level: 3-5
Description: Math Curse is a humorous book where a boy wakes up and goes through his entire week thinking about everything in terms of math. He explores his own world by putting in into a word problem or equation. In the end, the reader has a better understanding of how math is all around them.
Suggested readng strategy: With a book like this, it is difficult to tell what the point or main idea of the story is. By using the Main idea strategy, students will be able to keep track of the smaller ideas throughout the story and then put them together to come up with a main idea for the entire story. By understanding the main idea students will be able to comprhend the story.

Michelle Bonnetti
Book: Ten Rosy Roses
Citation: Merriam, Eve. (1999). Ten Rosy Roses. NY. HarperCollins.
Reading Level: DRA: 5-6 Guided Reading: D
Description: This book is about kids picking roses from a group of 10 one at at time. It teaches kids how to count backwards from 10 to 1.
Suggested Reading Strategy: I would use Look-Backs as Fix-It Strategies for this book. This book is recommended for younger students who are learning how to count backwards, but some of the words may be difficult. Students could use clues from the text and pictures to figure out words they are unfamiliar with.

Kayleigh Shaw
Book: The M&M's Addition Book
Citation: McGrath, Barbara Barbieri. (2004). The M&M's Addition Book. Watertown, MA: Charlesbridge.
Reading Level: Guided Reading- NR; Grade Level- 2.5
Description: Students learn how to estimate, group/organize, count objects, add, regroup, and add using tens and ones through this book. This book contains text with the proper terms regarding these math processes and pictures to help students understand them.
Suggested Literacy Strategy: Students can use the monitor, question, and repredict strategy when reading this book. The book calls for estimation at times, which can be similar to predicting in literature. Students then can use their knowledge of addition they gain throughout the book to evaluate their estimation/prediction and constantly alter their estimations. They will also gain the ability to check if their predictions were correct through the knowledge they gain.

Liz Kalajian
Book: Money
Citation: Pistoia, S. (2003). Money. Chanhassen: The Child’s World.
Description: Introduces the concept of money along with the values of different coins. Demonstrates the importance of knowing about money by showing real world examples that the students can identify with and relate to. The real life illustrations in the book can be helpful to activate prior knowledge as well as engage the students in learning about money.
Reading Level: DRA: 18-20, Guided Reading: J, Grade Level: 1-2
Suggested Literacy Strategy: Since this math picture book deals with the topic of money and real world examples the readers could use the literacy strategy of monitoring, questioning, and repredicting. This literacy strategy would be useful for the readers because it allows them to observe and see how money can be used and why, then it provides real math problems for the students to complete, and then it shows them the answers. Monitoring, questioning, and repredicting is a perfect strategy for the readers to use with this particular book because it allows them to solve the math problems efficiently while retaining the concepts.

Casey Caruso
Book: Math for All Seasons by Greg Tang
APA Citation: Tang, G. (2002). Math for All Seasons. New York, NY: Scholastic Press.

Reading Level: Guided Reading= L
Suggested Literacy Strategies: The main idea strategy would be good to use in this book. At the end of every riddle, the author, Greg Tang, suggests creative ways children can solve the problem to make it easier for them. If the children feel as though they need to take the long way to solve a problem, by counting every time, they will not understand they can get the answer much quicker.
Description: This math picture book has a different math riddle for kids to solve on each page. Every riddle in Math for All Seasons poses a problem. The kids can solve each riddle by either counting, or they can use the author’s suggested techniques at the bottom of each page to find the answer. This is a fun way for kids to enjoy math! Greg Tang makes it even more fun by rhyming the last word in every sentence on each page!


Lauren Masco
Book: One More Bunny
Citation: Walton, R. (2000). One more bunny. New York, NY: Lothrop, Lee & Shepard Books.
Reading Level: DRA: 11-12 Guided Reading: G Grade Level: 1.5
Description: It is a math picture book that explains to young math students the concept of adding from 1 to 10 by using bunnies. Each page depicts a number of bunnies, starting with 1, and gives a rhyme describing the scene. Each page ends with the phrase "here comes one more bunny." On each page, the addition problem is shown, first using pictures of bunnies, then using the actual numbers. All possible ways of adding to a number are shown.
Suggested Literacy Strategy: The predicting strategy would be appropriate for this book, because when read aloud students can predict how many bunnies will be on the next page. They can also predict and discuss the different ways to make a number by adding.

Alli Clare
Title: 1 2 3 What do you see? by Arlene Alda
Citation: Alda, A. (1998). 1 2 3 What Do You See?. Berkeley, California: Tricycle Press.
Description: A simple picture book that uses pictures taken of everyday life items that, when looked at closely, one can see numbers. For instance a bagel cut in half and placed one on top of the other makes an 8. The author shows the numbers 1 through 10, twice, with pictures from all walks of life.
Reading Level:
Grade: 1.3
DRA: 7-8
Guided Reading: E
Suggested Literacy Strategy: This is a difficult book to put with a reading strategy because it doesn’t contain any words, simply numbers and pictures. I would have students make connections with this book, by looking at items in their everyday lives and seeing if they can find numbers hidden within things.


Erin Jackson

Book: How Much Is A Million? by David M. Schwartz
Citation: Schwartz, D. (1985). How Much Is A Million? New York, NY: Scholastic Book Services.
Reading Level: DRA: 24, Guided Reading: K, Grade Level: 2.1
Description: Marvelosissimo the Mathematical Magician helps readers conceptualize and visualize one million, one billion, and one trillion. Large numbers can be difficult for young children but the words and illustrations can help children understand just how big these numbers are.

Suggested Literacy Strategies: Summarizing and drawing conclusions can be taught with this math picture book. Large numbers can be difficult for young students so summarizing the main concepts of the book will help students understand them better. In addition, at the end of the book, students can begin to draw conclusions about the numbers one million, one trillion, and one billion, which may be new ideas to them.


Gianna Seidler
Book Title: A Very Improbable Story by Edward Einhorn
Citation: Einhorn, E. (2008). A Very Improbably Story. Watertown, MA: Charlesbridge.
Reading Level: DRA: 24, Guided Reading: K, Grade: 2.5
Description:
This picture book introduces the concept of probability using a comical storyline, as it tells the story of boy named Ethan who wakes up with a talking cat on his head. Upon waking up, the cat tells Ethan that he will only move if Ethan wins probability game. After trying different tasks to rid himself of the cat, Ethan yields to the cats demands and decides to play the game. They then collect a variety of everyday items found around the house, such coins, socks and marbles, in order to use for the game. As they play, Ethan transforms from a careless guesser to a true problem solver with a sense of odds and outcomes. As these hilarious events unravel, readers are able to witness the improbability and probability of certain events using items that relate to their own lies and therefore are easier to understand.
Suggested Literacy Strategies: In order to help students grasp the concept of probability while also improving their literacy skills, the literacy strategy of predicting would suitably accompany this book. As the story unfolds and the students witness Ethan's antics, they can be taught, and eventually asked, to use clues in order to anticipate meaning. This can be done by first modeling how to predict the probability of the next experiment and event in the story, then scaffolding until the students can accomplish this task independently.


Christina Marino

Title: Pie for Piglets
Citation: Dahl, M., (2005). Pie for Piglets. Minneapolis: Picture Window Books.
Reading Level: K-2
Description: This picture book shows how to count by twos. It is the story of two piglets who are making a pie, so every ingredient that they put in is an even number, and the number of ingredients they put in increases by two.
Literacy Strategy: Predicting would be a good strategy to use. They could predict the number of items will go into the pie next. This way, they can figure out the pattern of even numbers and understand how to count by twos.


Margaret Molloy
Fraction Action
By Loreen Leedy
Citation: Leedy L. (1994). Fraction Action. New York: Holiday House.
Suggested Grade Level: 3-5
Summary: This book is all about fractions. It follows Miss Prime’s (pun intended!) classroom learning fractions. The book begins by just introducing halves and then goes into thirds and fourths. It also goes into how to make whole sets into fractions. The book is good because it uses real life examples and instruction.
Suggested Literacy Strategy: You could have students use go back and fix it. This book builds on different ideas about fractions, since it mimics students learning about fractions over a few days. When reading the book students can read things and go back in the book to find meaning.

Cynthia Antunes
Title: How High Can a Dinosaur Count? And Other Math Mysteries by Valorie Fisher
Citation: Fisher, Valorie. (2006). How High Can a Dinosaur Count? And Other Math Mysteries. New York, NY: Random House Inc.
Reading Level: DRA: 20 Guided Reading: NR Grade Level Equivalent: 4.6
Description: This book makes solving math problems lots of fun. On each page a short little word problem is presented as a brief story. The vocabulary and words used are fun and make the stories quite interesting. To accompany the word problem is an illustration which helps the student solve the word problem. At the end of the book, there are a few more math problems and word problems.
Suggested Comprehension Strategy: The strategy that works the best with this book is the look-back and fix-it strategy. As students read the book they must solve word problems. Before moving on, it is important that the students look-back or check their answers. They can reread the problem to make sure they did the appropriate computation or use the illustration for additional help.

Jasmine Martin
Title:
I Knew Two Who Said Moo: A Counting and Rhyming Book
Citation: Barrett, J. (2000).
I Knew Two Who Said Moo: A Counting and Rhyming Book. New York, NY: Simon & Schuster Children's Publishing.
Reading Level: DRA: 11-12; Guided Reading: G
Description: This is a silly rhyming book that also teaches children how to count to ten. The book stretches the readers imagination and while also teaching the concept of counting.
Suggested Reading Strategy: A good strategy to use for this book is predicting. Students can predict the numbers coming up on the next page as well as use context clues to predict the rhyming word on the next line.